2014/05/30 by F. Bastianelli, A. Huet, C. Schubert +2 · 11 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Feynman diagram #Feynman graph #Formalism (music) #Massless particle #Particle physics theoretical and experimental studies #Propagator #Scalar (mathematics) #Scalar field #Scalar field theory #hep-ph #hep-th
paper · pdf · doi:10.1007/jhep07(2014)066
published in Journal of High Energy Physics 2014(7) (Springer Nature) · 39 pages, 10 pdf figures
arxiv created 2014/05/30 · openalex publication_date 2014/07/01 · arxiv updated 2015/06/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We use the worldline formalism to derive integral representations for three classes of amplitudes in scalar field theory: (i) the scalar propagator exchanging N momenta with a scalar background field (ii) the “half-ladder” with N rungs in x-space (iii) the four-point ladder with N rungs in x-space as well as in (off-shell) momentum space. In each case we give a compact expression combining the N! Feynman diagrams contributing to the amplitude. As our main application, we reconsider the well-known case of two massive scalars interacting through the exchange of a massless scalar. Applying asymptotic estimates and a saddle-point approximation to the N-rung ladder plus crossed ladder diagrams, we derive a semi-analytic approximation formula for the lowest bound state mass in this model.